Finite Group Databasebeta

← #19145078

Subgroups — #19145078

Order 5504.

596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063351C211yesmaximal, characteristic, complemented
2C2×#13063350C211yesmaximal, characteristic, complemented
3C2×#13063345C211yesmaximal, characteristic, complemented
4C22×#10621882C211yesmaximal, characteristic, complemented
5#14583468C211yesmaximal, characteristic, complemented
6#14583289C212yesmaximal, complemented
7#14583286C212yesmaximal, complemented
8#14583281C212yesmaximal, complemented
9#14583275C212yesmaximal, complemented
10#14582855C211yesmaximal, characteristic, complemented
11C43×#535C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic
13C22×D172C2211yescharacteristic
14#13063351—24no—
15#13063350—24no—
16#13063345—24no—
17C2×#10621885C2211yescharacteristic, complemented
18C2×#10621883C2211yescharacteristic, complemented
19C2×#10621883C2212yescomplemented
20C2×#10621884C2211yescharacteristic, complemented
21C2×#10621884C2212yescomplemented
22C2×#10621882—24no—
23C2×#10621882C2212yes—
24C2×#10621882C2212yes—
25C2×#10621882C2211yescharacteristic, complemented
26C2×#10621882C2212yescomplemented
27C2×#10621882C2212yescomplemented
28C2×#10621877C2211yescharacteristic
29C22×C43⋊C8C2211yescharacteristic
30#13063322C2212yescomplemented
31#13063313C2212yescomplemented
32#13063300—22no—
33#13063295—22no—
34#13063236C2212yescomplemented
35C4×C43⋊C8C2212yescomplemented
36C2×#41×C43C2211yescharacteristic
37C22×D4×C43C2211yescharacteristic
38#127×C43C2212yescomplemented
39#124×C43C2212yescomplemented
40#121×C43—22no—
41#120×C43—22no—
42#117×C43C2211yescharacteristic
43C24×C43—21no—
44C23×D43—21no—
45#41×C43—22no—
46#41×C43—22no—
47C2×Q8×C43C2311yescharacteristic
48C2×D4×C43—21no—
49C2×D4×C43—24no—
50C2×D4×C43—21no—
51C2×D4×C43—22no—
52C2×D4×C43—22no—
53C2×D4×C43C2312yes—
54C2×D4×C43C2311yescharacteristic
55C22×C4×C43—21no—
56C22×C4×C43C2311yescharacteristic
57C2×C22⋊D43—21no—
58#10621898—22no—
59#10621898—22no—
60C2×D172—21no—
61C2×D172—24no—
62C2×D172—22no—
63C2×D172—22no—
64C2×D172C2312yes—
65C2×D172C2311yescharacteristic
66C2×C4×D43—21no—
67C2×Dic86C2311yescharacteristic
68C4⋊C4×C43D412yes—
69C22⋊C4×C43—24no—
70C22⋊C4×C43D412yes—
71C42×C43C2312yes—
72#10621885—22no—
73#10621884—22no—
74#10621884—24no—
75#10621883—22no—
76#10621883—24no—
77#10621882—24no—
78#10621882—24no—
79#10621882—22no—
80#10621882—24no—
81#10621882—24no—
82(C2×D43)⋊C4—24no—
83#10621877D414yescomplemented
84C2×C43⋊C8D414yescomplemented
85C2×C43⋊C8C2311yescharacteristic
86C2×C43⋊C8C2312yes—
87C2×C43⋊C8C2311yescharacteristic
88C23×C43—22no—
89C23×C43—21no—
90C23×C43—42no—
91C23×C43—82no—
92C23×C43C2×D411yescharacteristic
93C22×D43—22no—
94C22×D43—21no—
95C22×D43—42no—
96C22×D43—82no—
97Q8×C43—21no—
98Q8×C43—21no—
99D4×C43—22no—
100D4×C43—21no—
101D4×C43—22no—
102D4×C43—21no—
103D4×C43—42no—
104D4×C43—42no—
105D4×C43—84no—
106C2×C4×C43—21no—
107C2×C4×C43—42no—
108C2×C4×C43C2×D412yes—
109C2×C4×C43C2×D412yes—
110C2×C4×C43C2×D414yes—
111C2×C4×C43C2×D411yescharacteristic
112C2×C4×C43C2411yescharacteristic
113C22⋊D43—42no—
114C2×Dic43—21no—
115D172—22no—
116D172—21no—
117D172—22no—
118D172—21no—
119D172—42no—
120D172—84no—
121C4×D43—42no—
122Dic86—21no—
123Dic86—21no—
124C43⋊C8C2×D412yes—
125C43⋊C8C2×D412yes—
126C43⋊C8C2×D414yes—
127C22×C43—22no—
128C22×C43—42no—
129C22×C43—41no—
130C22×C43—44no—
131C22×C43—42no—
132C22×C43—84no—
133C22×C43#12712yes—
134C22×C43C22×D411yescharacteristic
135C2×D43—42no—
136C2×D43—41no—
137C2×D43—44no—
138C2×D43—42no—
139C2×D43—84no—
140C4×C43—24no—
141C4×C43—41no—
142C4×C43#12712yes—
143C4×C43C22×D411yescharacteristic
144C4×C43C22×D411yescharacteristic
145Dic43—41no—
146#3155—431nomaximal, Sylow
147C2×C43—22no—
148C2×C43—81no—
149C2×C43—82no—
150C2×C43C2×#12711yescharacteristic
151C2×C43#57612yes—
152D43—81no—
153D43—82no—
154C2×AGL(1,ℤ/8)—431no—
155C2×AGL(1,ℤ/8)—431no—
156C2×#135—431no—
157C22×D8—431no—
158#535—431no—
159#535D4311yescharacteristic, complemented
160#496—432no—
161#496—432no—
162#495—432no—
163#493—432no—
164#405—431no—
165C43#315511yescharacteristic, complemented, Sylow
166C2×#41—431no—
167C2×#41C2×D4311yescharacteristic
168C22×D4—431no—
169C22×D4C2×D4311yescharacteristic
170AGL(1,ℤ/8)—864no—
171AGL(1,ℤ/8)—864no—
172#135—864no—
173C2×Q16—431no—
174C2×SD16—431no—
175C2×SD16—432no—
176C2×SD16—431no—
177C2×SD16—432no—
178C2×D8—432no—
179C2×D8—432no—
180C2×D8—431no—
181C2×D8—432no—
182C2×D8—432no—
183C2×D8—864no—
184C2×M16—431no—
185C22×C8—431no—
186#127—432no—
187#127C2×D4312yescomplemented
188#124—432no—
189#124C2×D4312yescomplemented
190#121—22no—
191#121—862no—
192#120—22no—
193#120—862no—
194#117C2×D4311yescharacteristic
195#97—432no—
196C4×C8—432no—
197C24—21no—
198C24—861no—
199#41—22no—
200#41—22no—
201#41—862no—
202#41—862no—
203C2×Q8—431no—
204C2×Q8C22×D4311yescharacteristic
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—24no—
210C2×D4—432no—
211C2×D4—431no—
212C2×D4—861no—
213C2×D4—862no—
214C2×D4—862no—
215C2×D4—864no—
216C2×D4—861no—
217C2×D4C22×D4312yes—
218C2×D4C22×D4311yescharacteristic
219C22×C4—21no—
220C22×C4—861no—
221C22×C4C22×D4311yescharacteristic
222Q16—862no—
223SD16—862no—
224SD16—864no—
225SD16—862no—
226SD16—864no—
227D8—864no—
228D8—864no—
229D8—862no—
230D8—864no—
231D8—864no—
232M16—434no—
233C2×C8—434no—
234C2×C8—431no—
235C2×C8—432no—
236C2×C8—431no—
237C4⋊C4C22⋊D4312yes—
238C22⋊C4—24no—
239C22⋊C4—864no—
240C22⋊C4C22⋊D4312yes—
241C42C22×D4312yes—
242C23—22no—
243C23—21no—
244C23—42no—
245C23—82no—
246C23—862no—
247C23—861no—
248C23—3442no—
249C23—1722no—
250C23C2×C22⋊D4311yescharacteristic
251Q8—21no—
252Q8—21no—
253Q8—861no—
254Q8—861no—
255D4—22no—
256D4—21no—
257D4—22no—
258D4—21no—
259D4—42no—
260D4—42no—
261D4—84no—
262D4—862no—
263D4—861no—
264D4—862no—
265D4—861no—
266D4—3444no—
267D4—1722no—
268D4—1722no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—861no—
272C2×C4—1722no—
273C2×C4D4×D4312yes—
274C2×C4D4×D4312yes—
275C2×C4C2×C22⋊D4314yes—
276C2×C4C2×C22⋊D4311yescharacteristic
277C2×C4C23×D4311yescharacteristic
278C8—432no—
279C8—432no—
280C8—434no—
281C22—22no—
282C22—41no—
283C22—42no—
284C22—42no—
285C22—44no—
286C22—84no—
287C22—3444no—
288C22—1721no—
289C22—1722no—
290C22—1722no—
291C22—1724no—
292C22#1306332112yes—
293C22C22×C22⋊D4311yescharacteristic
294C4—24no—
295C4—41no—
296C4—1721no—
297C4#1306332112yes—
298C4C2×D4×D4311yescharacteristic
299C4C2×D4×D4311yescharacteristic
300C2—22no—
301C2—82no—
302C2—81no—
303C2—3442no—
304C2—3441no—
305C2C2×#1306332111yescharacteristic
306C2#1458370212yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#535C2
socleC22×C43C22×D4
hypercenter#535D43
hypocenterC43#3155
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#13063351C2semidirect
2. C2×#13063350C2semidirect
3. C2×#13063345C2semidirect
4. C22×#10621882C2semidirect
5. #14583468C2semidirect
6. #14583289C2semidirect
7. #14583286C2semidirect
8. #14583281C2semidirect
9. #14583275C2semidirect
10. #14582855C2semidirect
11. C43×#535C2semidirect
17. C2×#10621885C22semidirect
18. C2×#10621883C22semidirect
19. C2×#10621883C22semidirect
20. C2×#10621884C22semidirect
21. C2×#10621884C22semidirect
25. C2×#10621882C22semidirect
26. C2×#10621882C22semidirect
27. C2×#10621882C22semidirect
30. #13063322C22semidirect
31. #13063313C22semidirect
34. #13063236C22semidirect
35. C4×C43⋊C8C22semidirect
38. #127×C43C22semidirect
39. #124×C43C22semidirect
83. #10621877D4semidirect
84. C2×C43⋊C8D4semidirect
159. #535D43semidirect
165. C43#3155semidirect
187. #127C2×D43semidirect
189. #124C2×D43semidirect